1994 Fiscal Year Final Research Report Summary
Topologs of manifolds and mathematical plysics
| Project/Area Number |
05640105
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
KONO Akira Kyoto University, Fac.Sci., Professor, 理学部, 教授 (00093237)
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| Co-Investigator(Kenkyū-buntansha) |
NOMURA Takaaki Kyoto University, Fac.Sci., Associated Professor, 理学部, 助教授 (30135511)
FUKAYA Kenji Kyoto University, Fac.Sci., Professor, 理学部, 教授 (30165261)
NISHIDA Goro Kyoto University, Fac.Sci., Professor, 理学部, 教授 (00027377)
MARUYAMA Masaki Kyoto University, Fac.Sci., Professor, 理学部, 教授 (50025459)
UENO Kenji Kyoto University, Fac.Sci., Professor, 理学部, 教授 (40011655)
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| Project Period (FY) |
1993 – 1994
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| Keywords | free loop space / K-theor / Moise function / Morse homotopy / Quantun homotopy type / conformal field thery / vector bmdle |
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| Research Abstract |
The reserch results supported by Grants in Aid for Scientific Reserch (C) 05640105 consist of the following
1. Free loop group : det G be a compact, connected diegroup, LAMBDAG the space of free loops on G and p a prine. Then the following two conditions are equrialent :
(1) The integral cohomology of G is p-toscn free
(2) H^* (BLAMBDAG : */p)*H^* (BG : */p) <cross product> H^* (G : */p) as an algeha.
a similon resutt for the Dwyer-Wilkerson H-space is also obtained.
2. Infinite dimensional die groups : Topolegs of infinite dimesional die group (gauze groups)
3. Morse homotopy type : det M be a conysact manifold and f : M*IR a Morse function. The homotopy type of M can be cletermined by f.Fukaya dofined a categary by f and described the quantum homotopy type of a syinplectic monifolds. I oftainea a method to describe the homotopy type of M by f, Morsover Ueno studiea confomal field theoy using algehaie geometory and Maruyama studied classifying spaces, moduli of verion connections and modubi of vectr bmdles.
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